You are buying a small one-bedroom condo in Boston for $400,000, to be financed

Question

You are buying a small one-bedroom condo in Boston for $400,000, to be financed with two loans. The first is with the Northeastern University subsidized loan with a fixed interest rate of 6% for $200,000, with equal monthly payments for 20 years. The other loan (for the remaining amount of money needed) was provided for by a local bank with an initial interest of 8%, also payable each month for 20 years. The non-Northeastern University loan is an Adjustable Rate Mortgage (ARM). ARMs have an interest rate that varies, depending on the PRIME interest rate. Your interest rate increases and decreases exactly as how the PRIME rate changes.

Your monthly budget is that you can at most afford $3500 in montly payment to your mortgage. If after two years, the expected value of the PRIME rate is expected to increase by 4% and have a standard deviation of 0.75%, what is the probability that your house will be foreclosed because you can't afford to make payments?

Explanation / Answer

We have two loans and we first need to find out the amount of monthly payment on each loan after PRIME Rate hike

Loan amount Interest rate Monthly Payment

200,000 4% 1211.96

200,000 12% 2164.29

Total monthly Payment 3376.25

Affordable ayment = 3500

Standard Deviation = 200000 x 0.0075 = 1500

probability of default = 1- P(X)

= 1- P((3500-3376.25)/1500))

= 1- P( 0.0825)

we need to search the value of 0.0825 in the Zvalue table.

=1- 0.532875

probability of default = 46.71%

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